Sampling

1. Sampling

2. Sampling Issues Sampling Terminology Probability in Sampling Probability Sampling Designs Non-Probability Sampling Designs Sampling Distribution

3. Sampling Terminology

4. Two Major Types of Sampling Methods uses some form of random selection requires that each unit have a known (often equal) probability of being selected selection is systematic or haphazard, but not random Probability Sampling Non-Probability Sampling

5. Groups in Sampling Who do you want to generalize to?

6. Groups in Sampling The Theoretical Population

7. Groups in Sampling The Theoretical Population What population can you get access to?

8. Groups in Sampling The Theoretical Population The Study Population

9. Groups in Sampling The Theoretical Population The Study Population How can you get access to them?

10. Groups in Sampling The Theoretical Population The Study Population The Sampling Frame

11. Groups in Sampling The Theoretical Population The Study Population The Sampling Frame Who is in your study?

12. Groups in Sampling The Theoretical Population The Study Population The Sampling Frame The Sample

13. Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample

14. Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample

15. Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample

16. Where Can We Go Wrong? The Theoretical Population The Study Population The Sampling Frame The Sample

17. Statistical Terms in Sampling Variable

18. Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility

19. Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility Statistic

20. Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility Statistic Average = 3.72 sample

21. Statistical Terms in Sampling Variable 1 2 3 4 5 responsibility Statistic Average = 3.72 sample Parameter

22. Statistical Terms in Sampling Variable 1 2 3 4 5 response Statistic Average = 3.72 sample Parameter Average = 3.75 population

23. Statistical Inference • Statistical inference: make generalizations about a population from a sample. • A population is the set of all the elements of interest in a study. • A sample is a subset of elements in the population chosen to represent it. • Quality of the sample = quality of the inference • Would this class be a good representation of all Persian Doctors? Why or why not? This class would not be a good sample of all Persian Dentists, we are more interested in research methodology, so we are different!!

24. sample sample sample The Sampling Distribution

25. sample sample sample 5 5 5 0 0 0 5 5 5 0 0 0 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 The Sampling Distribution

26. sample sample sample 5 5 5 0 0 0 5 5 5 0 0 0 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 The Sampling Distribution Average Average Average

27. sample sample sample 5 5 5 0 0 0 5 5 5 0 0 0 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 1 5 1 0 5 0 3 . 0 3 . 2 3 . 4 3 . 6 3 . 8 4 . 0 4 . 2 4 . 4 The Sampling Distribution Average Average Average ...is the distribution of a statistic across an infinite number of samples The Sampling Distribution...

28. Random Sampling

29. Types of Probability Sampling Designs • Simple Random Sampling • Stratified Sampling • Systematic Sampling • Cluster Sampling • Multistage Sampling

30. Some Definitions • N = the number of cases in the sampling frame • n = the number of cases in the sample • NCn = the number of combinations (subsets) of n from N • f = n/N = the sampling fraction

31. Simple Random Sampling • Objective - select n units out of N such that every NCn has an equal chance • Procedure - use table of random numbers, computer random number generator or mechanical device • can sample with or without replacement • f=n/N is the sampling fraction

32. Simple Random Sampling Example: • People who subscribe Novin Pezeshki last year • People who visit our site • draw a simple random sample of n/N

33. Simple Random Sampling List of Residents

34. Simple Random Sampling List of Residents Random Subsample

35. Stratified Random Sampling • sometimes called "proportional" or "quota" random sampling • Objective - population of N units divided into non-overlapping strata N1, N2, N3, ... Ni such that N1 + N2 + ... + Ni = N, then do simple random sample of n/N in each strata

36. Stratified Sampling • The population is first divided into groups called strata. If stratification is evident • Example: medical students; preclinical, clerckship, internship • Best results when low intra strata variance and high inter strata variance • A simple random sample is taken from each stratum. • Advantage: If strata are homogeneous, this method is “more precise” than simple random sampling of same sample size • As precise but with a smaller total sample size. • If there is a dominant strata and it is relatively small, you can enumerate it, and sample the rest.

37. Stratified Sampling - Purposes: • to insure representation of each strata - oversample smaller population groups • sampling problems may differ in each strata • increase precision (lower variance) if strata are homogeneous within (like blocking)

38. Stratified Random Sampling List of Residents

39. Stratified Random Sampling List of Residents surgical medical Non-clinical Strata

40. Stratified Random Sampling List of Residents surgical medical Non-clinical Strata Random Subsamples of n/N

41. Systematic Random Sampling Procedure: • number units in population from 1 to N • decide on the n that you want or need • N/n=k the interval size • randomly select a number from 1 to k • then take every kth unit

42. Systematic Random Sampling • Assumes that the population is randomly ordered • Advantages - easy; may be more precise than simple random sample • Example - Residents study

43. Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 N = 100

44. Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 N = 100 want n = 20

45. Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 N = 100 want n = 20 N/n = 5

46. Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 N = 100 want n = 20 N/n = 5 select a random number from 1-5: chose 4

47. Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 429 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 934 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 1439 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 1944 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 244974 99 25 50 75 100 N = 100 want n = 20 N/n = 5 select a random number from 1-5: chose 4 start with #4 and take every 5th unit

48. Cluster Sampling • The population is first divided into clusters • A cluster is a small-scale version of the population (i.e. heterogeneous group reflecting the variance in the population. • Take a simple random sample of the clusters. • All elements within each sampled (chosen) cluster form the sample.

49. Cluster Random Sampling • Advantages - administratively useful, especially when you have a wide geographic area to cover • Example: Randomly sample from city blocks and measure all homes in selected blocks

50. Cluster Sampling vs. Stratified Sampling • Stratified sampling seeks to divide the sample into heterogeneous groups so the variance within the strata is low and between the strata is high. • Cluster sampling seeks to have each cluster reflect the variance in the population…each cluster is a “mini” population. Each cluster is a mirror of the total population and of each other.